Question
In: Finance
a company has two bonds outstanding. the first mature after five years and has a coupon...
a
company has two bonds outstanding. the first mature after five
years and has a coupon rate of 8.25%. the second matures after 10
years and has a coupon rate of 8.25%. Interest rates are currently
10 percent. what is the present price of each $1000 bond?
Solutions
Expert Solution
Bond-1:
Par Value of the bond = $1,000
Coupon rate = 8.25%
Therefore, annual coupon = 1000*8.25% =$82.50
Years to maturity = 5 years
YTM on bond (Current Interest Rate) = 10%
.
Price of the bond = Present value of coupons discounted at YTM + Present value of redemption value discounted at YTM
= 82.50*PVIFA(10%,5) + 1000*PVIF(10%,5)
= 82.50*3.7098 + 1,000*0.6209
= 306.0585 + 620.90
= $926.96
.
.
.
Note:-
PVIFA(10%,5) = 3.7098
PVIF(10%,5) = 0.6209
.
.
Bond-2:
Par Value of the bond = $1,000
Coupon rate = 8.25%
Therefore, annual coupon = 1000*8.25% =$82.50
Years to maturity = 10 years
YTM on bond (Current Interest Rate) = 10%
.
Price of the bond = Present value of coupons discounted at YTM + Present value of redemption value discounted at YTM
= 82.5*PVIFA(10%,10) + 1000*PVIF(10%,10)
= 82.5*6.1446 + 1,000*0.3855
= 506.9295 + 385.5
= $892.43
.
.
.
Note:-
PVIFA(10%,10) = 6.1446
PVIF(10%,10) = 0.3855
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